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Simplifying 148 = 16T2 + 64T Reorder the terms: 148 = 64T + 16T2 Solving 148 = 64T + 16T2 Solving for variable 'T'. Reorder the terms: 148 + -64T + -16T2 = 64T + -64T + 16T2 + -16T2 Combine like terms: 64T + -64T = 0 148 + -64T + -16T2 = 0 + 16T2 + -16T2 148 + -64T + -16T2 = 16T2 + -16T2 Combine like terms: 16T2 + -16T2 = 0 148 + -64T + -16T2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(37 + -16T + -4T2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(37 + -16T + -4T2)' equal to zero and attempt to solve: Simplifying 37 + -16T + -4T2 = 0 Solving 37 + -16T + -4T2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -9.25 + 4T + T2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + 4T + 9.25 + T2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + 4T + T2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + 4T + T2 = 0 + 9.25 4T + T2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 4T + T2 = 9.25 The T term is 4T. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4T + 4 + T2 = 9.25 + 4 Reorder the terms: 4 + 4T + T2 = 9.25 + 4 Combine like terms: 9.25 + 4 = 13.25 4 + 4T + T2 = 13.25 Factor a perfect square on the left side: (T + 2)(T + 2) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (T + 2) equal to 3.640054945 and -3.640054945.Subproblem 1
T + 2 = 3.640054945 Simplifying T + 2 = 3.640054945 Reorder the terms: 2 + T = 3.640054945 Solving 2 + T = 3.640054945 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + T = 3.640054945 + -2 Combine like terms: 2 + -2 = 0 0 + T = 3.640054945 + -2 T = 3.640054945 + -2 Combine like terms: 3.640054945 + -2 = 1.640054945 T = 1.640054945 Simplifying T = 1.640054945Subproblem 2
T + 2 = -3.640054945 Simplifying T + 2 = -3.640054945 Reorder the terms: 2 + T = -3.640054945 Solving 2 + T = -3.640054945 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + T = -3.640054945 + -2 Combine like terms: 2 + -2 = 0 0 + T = -3.640054945 + -2 T = -3.640054945 + -2 Combine like terms: -3.640054945 + -2 = -5.640054945 T = -5.640054945 Simplifying T = -5.640054945Solution
The solution to the problem is based on the solutions from the subproblems. T = {1.640054945, -5.640054945}Solution
T = {1.640054945, -5.640054945}
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